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Volume 12, Issue 4
Numerical Study of Time-Fractional Telegraph Equations of Transmission Line Modeling

Wang Kong & Zhongyi Huang

East Asian J. Appl. Math., 12 (2022), pp. 821-847.

Published online: 2022-08

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  • Abstract

The stability and uniqueness of the solutions of time-fractional telegraph equations arising in the transmission line modeling are proved. The corresponding initial-boundary problems are then solved by a finite difference scheme. It is shown that the scheme is unconditionally stable and convergent. Computational efficiency of the method can be enhanced by transforming it into two finite volume schemes for solving two uncoupled time-fractional convection equations. Numerical experiments validate the theoretical results and show the efficiency of this approach even for the problems the solutions of which are not smooth at the initial moment.

  • AMS Subject Headings

65M10, 78A48

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COPYRIGHT: © Global Science Press

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@Article{EAJAM-12-821, author = {Kong , Wang and Huang , Zhongyi}, title = {Numerical Study of Time-Fractional Telegraph Equations of Transmission Line Modeling}, journal = {East Asian Journal on Applied Mathematics}, year = {2022}, volume = {12}, number = {4}, pages = {821--847}, abstract = {

The stability and uniqueness of the solutions of time-fractional telegraph equations arising in the transmission line modeling are proved. The corresponding initial-boundary problems are then solved by a finite difference scheme. It is shown that the scheme is unconditionally stable and convergent. Computational efficiency of the method can be enhanced by transforming it into two finite volume schemes for solving two uncoupled time-fractional convection equations. Numerical experiments validate the theoretical results and show the efficiency of this approach even for the problems the solutions of which are not smooth at the initial moment.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.070921.150222}, url = {http://global-sci.org/intro/article_detail/eajam/20886.html} }
TY - JOUR T1 - Numerical Study of Time-Fractional Telegraph Equations of Transmission Line Modeling AU - Kong , Wang AU - Huang , Zhongyi JO - East Asian Journal on Applied Mathematics VL - 4 SP - 821 EP - 847 PY - 2022 DA - 2022/08 SN - 12 DO - http://doi.org/10.4208/eajam.070921.150222 UR - https://global-sci.org/intro/article_detail/eajam/20886.html KW - Finite difference scheme, time-fractional telegraph equation, transmission line modeling, non-smooth initial value. AB -

The stability and uniqueness of the solutions of time-fractional telegraph equations arising in the transmission line modeling are proved. The corresponding initial-boundary problems are then solved by a finite difference scheme. It is shown that the scheme is unconditionally stable and convergent. Computational efficiency of the method can be enhanced by transforming it into two finite volume schemes for solving two uncoupled time-fractional convection equations. Numerical experiments validate the theoretical results and show the efficiency of this approach even for the problems the solutions of which are not smooth at the initial moment.

Wang Kong & Zhongyi Huang. (2022). Numerical Study of Time-Fractional Telegraph Equations of Transmission Line Modeling. East Asian Journal on Applied Mathematics. 12 (4). 821-847. doi:10.4208/eajam.070921.150222
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